you can do it with php and using a child (recommended):
This above the activity stream loop somewhere put this code:
$style_classes = array('style-a-class','style-b-class');
$style_index = 0;
Then this inside the li tag that gets looped through for each activity post:
<li <?php $s = $style_index%2; echo "class=$style_classes[$s]"; $style_index++; ?>>
Works great for any wp template not just a buddypress.